Interesting discussions about the foundations of economics.
A further difficulty with the barebones theory of rationality concerns the individuation of the objects of preference or choice. Consider, for example, data from multistage ultimatum games. Suppose A can propose any division of $10 between A and B. B can accept or reject A’s proposal. If B rejects the proposal, then the amount of money drops to $5, and B gets to offer a division of the $5 which A can accept or reject. If A rejects B’s offer, then both players get nothing. Suppose that A proposes to divide the money with $7 for A and $3 for B. B declines and offers to split the $5 evenly, with $2.50 for each. Behavior such as this is, in fact, common (Ochs and Roth 1989, p. 362). Assuming that B prefers more money to less, these choices appear to be a violation of transitivity. B prefers $3 to $2.50, yet declines $3 for certain for $2.50 (with some slight chance of A declining and B getting nothing). But the objects of choice are not just quantities of money. B is turning down $3 as part of “a raw deal” in favor of $2.50 as part of a fair arrangement. If the objects of choice are defined in this way, there is no failure of transitivity.
This plausible observation gives rise to a serious problem. Unless there are constraints on how the objects of choice are individuated, conditions of rationality such as transitivity are empty. A’s choice of X over Y, Y over Z and Z over X does not violate transitivity if “X when the alternative is Y” is not the same object of choice as “X when the alternative is Z”. John Broome (1991) argues that further substantive principles of rationality are required to limit how alternatives are individuated or to require that agents be indifferent between alternatives such as “X when the alternative is Y” and “X when the alternative is Z.”
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